2.2. Factores de riesgo y sus implicaciones
2.2.5 Riesgos laborales en la industria textil
Interest rates do influence house prices, but they cannot provide anything close to a complete explanation of the great housing market gyrations between 1996 and 2010. Over the long 1996-2006 boom, they cannot account for more than one-fifth of the rise in house prices. Their biggest predictive influence is during the 2000-2005 period, when long rates fell by almost 200 basis points. That can account for about 45% of the run-up in home values nationally during that half-decade span. However, if one is going to cherry-pick time periods, it also must be noted that falling real rates during the 2006-2008 price bust simply cannot account for the 10% decline in FHFA indexes those years.
There is no convincing evidence from the data that approval rates or down payment requirements can explain most or all of the movement in house prices either. The aggregate data on these variables show no trend increase in approval rates or trend decrease in down payment requirements during the long boom in prices from 1996-2006. However, the number of
applications and actual borrowers did trend up over this period (and fall sharply during the bust), which raises the possibility that the nature of the marginal buyer was changing over time.
Carefully controlling for that requires better and different data, so our results need not be the final word on these two credit market traits.
This leaves us in the uncomfortable position of claiming that one plausible explanation for the house price boom and bust, the rise and fall of easy credit, cannot account for the majority of the price changes, without being able to offer a compelling alternative hypothesis. The work of Case and Shiller (2003) suggests that home buyers had wildly unrealistic expectations about future price appreciation during the boom. They report that 83 to 95 percent of purchasers in 2003 thought that prices would rise by an average of around 9 percent per year over the next decade. It is easy to imagine that such exuberance played a significant role in fueling the boom.
Yet, even if Case and Shiller are correct, and over-optimism was critical, this merely pushes the puzzle back a step. Why were buyers so overly optimistic about prices? Why did that optimism show up during the early years of the past decade and why did it show up in some markets but not others? Irrational expectations are clearly not exogenous, so what explains them? This seems like a pressing topic for future research.
Moreover, since we do not understand the process that creates and sustains irrational beliefs, we cannot be confident that a different interest rate policy wouldn’t have stopped the bubble at some earlier stage. It is certainly conceivable that a sharp rise in interest rates in 2004 would have let the air out of the bubble. But this is mere speculation that only highlights the need for further research focusing on the interplay between bubbles, beliefs and credit market conditions.
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Appendix A: Simulation Methodology
This appendix presents our procedure for computing the price-rent ratio with stochastic interest rates.
As in the analytical model, the marginal consumer must be indifferent between renting and buying. If she rents, she pays an amount taken directly from equation 1 in the text:
1 1
1
1 .
We assume that the discount rate is determined at time t, and is constant over all j. Thus we
set . Whether we are in the ̂ 1 case or the ̂ 0 case, the
discounting is determined at time t and unchanged thereafter.
We further assume that grows at rate g. Thus the rental cost can be solved
analytically, and, as in the deterministic case, is
.
We define so that .
To compute the expected cost of homeownership (labeled ), we begin by taking the time-t expectation of equation 2 from the text:
1 1
1
1 1 1 1
1
We next split this up into two parts as follows: where
1 1 1 1 1 1 1 1 and 1 1 1 .
Note that is time-varying, but depends only on the current interest rate. This is because the
time-varying components, and , are known for all future periods as soon as the
current interest rate is known. (This is true whether is fixed or depends on the
current value of .)
But the expected discounted sale price, , is more complicated. It depends on the expectation of future prices, and these are not yet known.
Simulations with inelastic housing supply
When housing supply is inelastic, the equilibrium condition equates expected rent
payments with expected ownership costs. So we set , or . Thus
.
In order to solve out the price-rent ratio, we make one further assumption that guarantees a
consistent relationship between / and the interest rate . We assume that future prices
relate to the interest rate in the same way that current prices do; i.e., there is a constant price-rent relationship given by
.
That is, the price-rent ratio can only depend on the current interest rate. This assumption seems reasonable, since a solution for the price-rent ratio would not make much sense if it varied with the interest rate in a different manner from the future price-rent ratio.
This assumption implies that , but since grows at rate g,
1 . Thus we can rewrite as a function only of r:
1
1 1 1 .
Given this definition of , the price-rent function can be written as:
The challenge is now very explicit: the unknown function appears on both sides of this
equation. We solve for using numerical simulations.
For each simulation, we begin with two straightforward calculations. First, we compute for the appropriate parameters and , and using the appropriate assumption about discount
rates. Second, we calculate using its explicit definition, given above. We approximate the
for the interest rate. For each path, we compute the discounted sum. Finally, we average over these simulations.27
In order to solve for , we guess a solution and iterate. At each iteration, we calculate
using the previous guess of the price-rent function · , and 1,500 simulated interest
rate paths. We also approximate this infinite sum by calculating the series going 1,000 years
forward from t. The discounted sum of these expectations yields a value for each on the
interest rate grid. Combining this with the appropriate and yields our next guess for the
function, denoted . We repeat this iterative process until the function converges;
convergence is defined as max / 0.001.
Simulations with elastic housing supply
When we consider elastic housing supply, the equilibrium condition relates house prices
to their flow value rather than to rental prices. We normalize the construction costs to 1, and
scale prices by the growth factor; i.e., / 1 and / 1 . Thus instead of
, our equilibrium condition becomes:
.
Using the housing supply equation, , we then have:
/
Similar to the assumption of a constant function for the price-rent ratio in the case with inelastic supply, we now assume that prices have a constant relationship to interest rates in all periods, so
1 for all j. We can therefore write
1 1 1 1 and hence / 27
Note that we discretize the Cox-Ingersoll-Ross process by using interest rates ranging from
0.05% to 14%, with grid size of 0.05%. We run 1,500 simulations for each starting value of on the grid. We calculate for each on this grid, and also use this grid to capture the distribution of future interest rates at each future year t+j.
where · denotes the previous guess of the function · . We then solve for in a similar
Appendix B: Mortgage approval coefficients
Applicant sex: Ethnicity:
Joint application 0.021 Asian ‐0.024
Female applicant 0.031 Black ‐0.151
Unknown 0.009 Hispanic ‐0.084
Native American ‐0.132 Note: Male applicant is omitted. Pacific Islander ‐0.099
Unknown ‐0.172
Quantile of income:
1 ‐0.224 Note: White is omitted.
2 ‐0.136 3 ‐0.098 4 ‐0.085 5 ‐0.054 6 ‐0.027 7 ‐0.039 8 ‐0.040 9 ‐0.008 10 ‐0.032 11 0.022 12 0.007 14 0.023 15 0.020 16 0.026 17 0.036 18 0.019 19 0.031 20 0.035 21 0.010 22 0.021 23 0.019 24 0.004 25 ‐0.018 Unknown 0.021
Note: Median quantile (13) is omitted.
Notes: Coefficients are reported from a linear probability model in which mortgage approval is regressed on the covariates reported above, a full set of Metropolitan Statistical Area dummies, and a full set of interactions between the income quantiles and applicant sex. The regression includes 13,920,695 mortgage applicants from the 2006 Home Mortgage Disclosure Act data. Applicants are dropped if they have an explicit federal guarantee from the FHA, VA, FSA, or RHS, if they withdrew the
application (following Munnell et al., 1996), or if they have invalid geographic coding.
Appendix C: Empirical Methods
Appendix C.1: One Instrument Estimation
We let and reflect the price and approval rates in area j at time t that have already
been orthogonalized with respect to other variables such as the metropolitan area and year fixed
effects. We then assume that and or and
. The OLS estimate, denoted , found by regressing price on approval yields:
1
,
which is greater than (for positive ) whenever 1 . If we let
1
,
or , it follows that solves 1 0. Thus
. We have estimated to be 0.26, and the estimated value of γ is 0.058. The ratio of the variance of prices (orthogonalized with respect to year and
metropolitan area fixed effects) to the variance of approval rates (orthogonalized with respect to the same variables) is 6.7. These suggest that must either equal -0.13 or 17.2, and 17.2 is
inadmissible since it would imply a negative value of .
Appendix C.2: The Use of Regulations-Year Interactions as Instruments
The net present value of an infinite horizon loan of one dollar at interest rate R, which has
a probability of defaulting equal to in each period, equals ∑ , where
is the bank’s discount rate, and is the recovery rate for defaulted loans (beyond paying
the last period’s interest). The zero profit condition then implies that , where
reflects the maximum default risk that the bank will take on, assuming that there is a maximum value of R (otherwise there would never be a maximum default risk).
Differentiating this expression with respect to the “global” interest rate tells us that
be the case. Moreover, if the derivatives of R and are independent of , the recovery rate,
then 0, so this effect will be stronger in places where the
recovery rate is higher. If we think that larger banks are more globally connected, then
Appendix D: Interest Rates and Housing Construction
Table D.1 repeats the regressions of Table 6 using construction, rather than housing, as the dependent variable. We use building permits as reported by the U.S. Census Bureau in its Manufacturing, Mining and Construction Statistics data, with the log of the national number
being the dependent variable in Table D.1’s specifications.28 Not only is construction
intrinsically interesting due to its impact on the larger economy, it also helps provide a check on our price results. Because construction statistics typically are better measured than house prices due a permit being required for each home, finding an economically and statistically strong link between interest rates and building activity would at least raise the possibility that the relatively
weak relationship between prices and rates is due to measurement in the former.29
Regressions (1) and (2) show the time series relationship between the ten year rate and
the logarithm of the number of single family permits in the country as a whole.30 The univariate
coefficient is -8.27, with a standard error or 4.26. As with prices, the interest rate elasticity falls dramatically when a time trend is included, as shown in column (2). Construction levels, as well as housing prices, have been trending upwards over the past three decades. The results in
columns (3) and (4) show no significant interest elasticities when we limit the sample to the period after 1985.
Regression (5) presents a changes-on-changes specification, yielding a coefficient of - 4.82 that is not precisely estimated. Regression (6) reports results when we estimate interest rate effects for low and high rate periods. Note that the results are the reverse of those for prices— there is a large effect of lowering interest rates from high levels, but not from low levels. Perhaps this has something to do with builders’ capacity to fund themselves changing discretely when rates fall from high levels, but not from low ones. In any event, building activity goes up
much more when rates fall a given amount from a high level rather than a low one.31 Finally, in
regression (8), we find that the Romer and Romer variable has a modest, but imprecisely estimated, correlation with new supply.
We have also estimated the analogues to Appendix Table D.1 for high versus low supply elasticity markets, using our quantity measure as the dependent variable. We never find a statistically or economically significant relationship in any specification. Thus, there is no evidence that interest rate sensitivity of quantities in the housing markets differs appreciably across markets by their supply side fundamentals.
28
The data are available electronically at http://censtats.census.gov/bldg/bldgprmt.shtml. 29
An independent impact is certainly possible, since builders may rely on financing for duration of their projects. 30
Not only is the interest rate impact on building activity interesting in its own right, but if one were willing to make a very specific assumption about the magnitude of the elasticity of housing supply (including that the elasticity is constant across areas), then the estimated elasticities reported in Appendix Table D.1 provide an alternative means of evaluating the house price-interest rate relationship. For example, if we were to accept Topel and Rosen’s (1986) national supply elasticity of two, we would expect the interest rate elasticity of construction to be approximately two